Chapter 78, Problem 1AR

To determine

(a)

Angle of rotation R.

Answer to Problem 1AR

The angle of rotation is $30°4^{\prime }$.

Explanation of Solution

Given:

Three view of compound-angular hole are shown below:

Concept used:

Expression for the angle of rotation is given below:

  $\tan R=\frac{\tan B}{\tan A}$ ...... (1)

Here, angle of the font view from the vertical axis is $A$, angle of the right side view from the vertical axis is $B$ and angle of rotation is $R$.

Calculation:

Angle of the front view from the vertical axis is calculated as follows:

From the above figure,

  $\begin{array}{l}\tan A=\frac{1.9}{2.2}\\ A=40.815°\end{array}$

Angle of the right-side view from the vertical axis is calculated as follows:

From the above figure,

  $\begin{array}{l}\tan B=\frac{1.1}{2.2}\\ B=26.565°\end{array}$

Substitute $40.815°$ for $A$ and $26.565°$ for $B$ in equation (1).

  $\begin{array}{c}\tan R=\frac{\tan 26.565°}{\tan 40.815°}\\ R=30.06865°\\ R=30°4^{\prime }\end{array}$

Thus, the angle of rotation is $30°4^{\prime }$.

Conclusion:

The angle of rotation is $30°4^{\prime }$.

To determine

(b)

Angle of tiltT.

Answer to Problem 1AR

The angle of tilt is $44°56^{\prime }$.

Explanation of Solution

Given:

Three view of compound-angular hole are shown below:

Concept used:

Expression for the angle of tilt is given below:

  $\tan T=\sqrt{{\tan }^{2}A+{\tan }^{2}B}$ ...... (2)

Here, angle of the font view from the vertical axis is $A$, angle of the right side view from the vertical axis is $B$ and angle of tilt is $T$.

Calculation:

Substitute $40.815°$ for $A$ and $26.565°$ for $B$ in equation (2).

  $\begin{array}{c}\tan T=\sqrt{{\tan }^2\left(40.815°\right)+{\tan }^2\left(26.565°\right)}\\ \tan T=\sqrt{0.74586+0.24999}\\ T=44.94055°\\ T=44°56^{\prime }\end{array}$

Thus, the angle of tilt is $44°56^{\prime }$.

Conclusion:

The angle of tilt is $44°56^{\prime }$.